Answer:
Explained
Explanation:
A) The total energy of the system is defined by the energy at maximum amplitude, which we'll call A. At that point, the energy of the system is
E = 1/2×m×A^2;
since energy is conserved, this is also the total amount of energy that the system ever has.
So at x=1/2A,
the potential energy of the system is 1/8×m×A^2
which is one-fourth of the system's total energy. Therefore, the remaining three-fourths is kinetic.
B) (i) Doubling the maximum amplitude will quadruple the total energy:
(ii) Doubling the maximum amplitude will double the maximum velocity
(iii) Doubling the maximum amplitude will double the maximum acceleration: m×a = -k(2A)
(iv) Doubling the maximum amplitude leaves the period unchanged:
(neither m nor k has changed).
Answer:
A. False
B True
C. False
D.False
E. True
F. False
G. False
H. False
I. True
Explanation:
A. False: The system being analyzed consists of the bug and the car. These are the two bodies involved in the collision.
B. True: The system being analyzed consists of the bug and the car
C. False: The magnitudes of the change in velocity are different from the car and the bug. The velocity of the bug changes from 0 to the velocity of the car, while there is no noticeable change in the velocity of the car
D.False: There is barely any change in the momentum of the car since the mass of the bug is very small.
E. True: Since the mass of the bug is small, and was initially at rest, the magnitude of the change in monentum will be large because the new velocity will be that of the car.
F. False: The system being analyzed consists of the bug and the car. Those are the two bodies involved in the collision
G. False: The car barely changes in velocity since the mass of the bug is small.
H. False: The car barely changes in momentum because the collision does not affect its speed so much. on the other hand the momentum change of the bug is large since its mass is small.
I. True: The bug which was initially at rest will begin moving with the velovity of the speeding car, while the car barely changes in its velocity
Answer:
b) in a direction that makes its potential energy decrease.
Explanation:
- As the electric field has the direction that would take a positive test charge under its sole influence, the positive test charge, will have an increase in its kinetic energy.
- Due to the conservation of energy, in absence of non-conservative forces, this increment must be equal and opposite to the change in electric potential energy, which will be always negative, independent of the sign of the charge.
Answer:
Explanation:
Given that,
Radius of solenoid R = 4cm = 0.04m
Turn per length is N/l = 800 turns/m
The rate at which current is increasing di/dt = 3 A/s
Induced electric field?
At r = 2.2cm=0.022m
µo = 4π × 10^-7 Wb/A•m
The magnetic field inside a solenoid is give as
B = µo•N•I
The value of electric field (E) can
only be a function of the distance r from the solenoid’s axis and it give as,
From gauss law
∮E•dA =qenc/εo
We can find the tangential component of the electric field from Faraday’s law
∮E•dl = −dΦB/dt
We choose the path to be a circle of radius r centered on the cylinder axis. Because all the requested radii are inside the solenoid, the flux-area is the entire πr² area within the loop.
E∮dl = −d/dt •(πr²B)
2πrE = −πr²dB/dt
2πrE = −πr² d/dt(µo•N•I)
2πrE = −πr² × µo•N•dI/dt
Divide both sides by 2πr
E =- ½ r•µo•N•dI/dt
Now, substituting the given data
E = -½ × 0.022 × 4π ×10^-7 × 800 × 3
E = —3.32 × 10^-5 V/m
E = —33.2 µV/m
The magnitude of the electric field at a point 2.2 cm from the solenoid axis is 33.2 µV/m
where the negative sign denotes counter-clockwise electric field when looking along the direction of the solenoid’s magnetic field.
